Alright alright I have a evil Monokuma mind, so this came to my mind easily-
The normal execution into plays with Monokuma hitting the red button, a message appearing that you were being executed. Like Maid Mom (Kirumi), you would run away from the execution, only to be chased into a freezer. Monokuma locked you in the freezer and makes you solve a puzzle, for every mistake, it gets colder faster. But the thing is, the puzzle is actually impossible, but you only realize it when you get the key to unlock the freezer door, the key is in a ice block. If you do manage to break it, when you try and unlock the door, you find out it's the wrong key. You eventually freeze to death and Monokuma makes popsicles :)